In the transverse gauge, the Cotton tensors were demonstrated to factorise into products of second-order operators (REF ) involving all partially massless values and, equivalently, into products of first-order operators (REF ) involving all depth-\(t\)  pseudo-masses (with both signs of helicity). This in turn demonstrates that the action (REF ) for conformal higher-spin gauge fields factorises, on an AdS\(_3\)  background, into wave operators associated with partially massless fields. This is in line with earlier results obtained in even dimensions [1]}, [2]}, [3]}, [4]}, [5]}, [6]}, [7]}, [8]}, [9]}, [10]}.
